1. My father drives me to school.

Question

2. I go to school in my father's car.
3. I go to school by my father's car.
[Can we use 'by' in the sentence?]

4. I go to school by car.
5. I drive a car to school.
6. I drive my car to school.
[Does #4 mean #5 or #6? When Father drives me to school, can we use #4?]

Answer 1

1 and 2 are fine.
3 isn't. To use "by" you'd be saying or writing something like these:
I go to school by car.
... by bicycle.
... by bike.
... by motor scooter.
... by bus.
etc.

4, 5, and 6 are all fine and basically mean the same thing.

And yes, if Father drives you to school, you can use #4.

Answer 2

No, you can't use #4 if your father drives you to school

Answer 3

My parents drive me to school by car.
Or
My parents drive me to school in car.
[Help me, thanks]

Answer 4

Car